Abstract
In this study, a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials. According to this theoretical approach, the microstructural-size (related to the volumetric content of fibres in fibre-reinforced concrete), the crack-size, and the size-scale effects on the Paris’ law and the Wöhler equation are presented within a unified mathematical framework. Relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. All these information are expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is herein elucidated.
Highlights
The assessment of the fatigue behaviour of quasi-brittle materials, such as plain or fibre-reinforced concrete (FRC), is important from the engineering point of view
A generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials
Relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. All these information are expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is elucidated
Summary
The assessment of the fatigue behaviour of quasi-brittle materials, such as plain or fibre-reinforced concrete (FRC), is important from the engineering point of view. The fatigue behaviour of quasi-brittle materials in bending or even in compression is not completely understood in terms of all the influential variables, such as the type of the loading cycle, cycling rate, structural size, crack length and, perhaps most important of all for FRC, fibres parameters. Note that Eq (9) has been derived from Eq (8) by choosing u , KIC and the plastic zone size as the main variables whose suitable combination provides a dimensionless number At this point, we want to see if the number of quantities involved in the relationship (9) can be reduced further from height. 3 , 4 , 5 and 8 (the same conditions apply to the dimensionless numbers as in the derivation of Eq (4)), obtaining: vf f
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